Force of 6" x 18" Steel Panel Weighing 3.25 Pounds Striking a Person

[expertplus]

This topic has been discussed before at this site, but there was never any agreement. I have a very specific situation that I hope I can get a concrete answer, including equations and a step-by-step solution in inch/pounds/seconds units.

A steel flat panel 6" X 18" weighing 3.25 pounds pivoted and fell 4 feet (center of gravity) striking a person flat on the head. What was the force that struck the person? This was an actual situation that raised a lump on the person's head.

 

[Filip Larsen]

I have not read the thread you refer to, but I will most likely just repeat what has been said there.

You cannot in general say what this (maximum or average) force will be without knowing a bit more. If we ignore friction from air you could model the impact itself as a more or less elastic collision transferring momentum and energy from the plate to the head. To do this you would need to know how elastic the collision is, either by measurements or by a more detailed model of the plate bending dynamics. The latter would also enable you to get a rough estimate of the collision time and forces involved if force really is what you want.

What conclusion are you hoping to make based on knowing this force? Could you reach this conclusion in other ways?

 

[ApuroopS]

Like filiplarsen has mentioned, you'll need more details for more accurate measurements...

but if you were to simplify the case,
by ignoring air resistance
you could calculate the speed of the plate just before it hit the head by the work-energy theorem.

it comes out to be approx 16 feet/second


and if you take the (plate+earth) as the system, you could calculate the impulse imparted to the plate by the mans head due to the collision. This impulse would be equal to the change in momentum of the plate.

momentum of the plate(just before hitting the man's head) = mass.velocity = 52 pound feet/second

momentum of plate(after hitting the man) = 0
{ assuming the plate comes to rest, the collision being completely inelastic }

so, impulse exerted = change in momentum = 52-0 = 52 pound feet/second

and by Newton's third law, since every action, has an equal and opposite reaction, the impulse acted on the plate, would be the same as the impulse on the mans head.

so impulse exerted on the mans head = 52 pound feet/second

and furthermore, if you can measure the time for which the head and the plate are in contact, you could calculate the force acting on the man's head by dividing the impulse by the contact time.

assuming, the plate was in contact with the man's head for 0.01 seconds,

then force acting on the man's head = impulse/contact time = 52/0.01 = 5200 pound feet/(second)^2

that's equivalent to a mass of about 162.5 pounds.


but this will vary from the real case, as all this is done assuming air resistance isn't present..
If you were to take that into consideration... Well, the problem would become much more complex.
And also, i randomly assumed the contact time to be 0.01 seconds
even a small difference in this can make quite a difference.

besides, loads of other factors will come into play, like the compression offered by the hair, angle of striking.. The actual elasticity of the collision etc etc..

(and I'm not familiar with the british system of units of force and momentum so i just stuck with the basics..)

and yes, sorry for the lack of proper equations, but i have no access to a pc as of now and am posting this from my cell phone..
Hope this helps.
Cheers.

 

[ApuroopS]

And i forgot to mention,
i also made an assumption that the plate is a point object with a mass of 3.25 pounds..
I guess that about covers it..